Figure REF (a) shows a three-dimensional representation of the interface at \(\tilde{t} = 0.89\) , coloured by the \(x\) -component velocity relative to the bubble nose, \(\tilde{u}_{ref,x} = (u_{x} - U_{b})/U_{b}\) . Figure REF (b) depicts the azimuthal component of the normalised vorticity field, \(\tilde{\omega }_{z} = \omega _{z}/(D/U_{a})\)  (top half), and the flow topology parameter, \(Q\)  (bottom half) as contour plots over an \((x,y)\)  plane for the three \(Ca\)  studied. Here, \(Q\) , which measures the influence of the bubble-liquid interface on the flow field and relates this information to the dominant flow type, is defined as follows
[1]}
\(Q = \frac{{D}^{2} - {O}^2}{{D}^{2} + {O}^2} = {\left\lbrace \begin{array}{ll}-1 & \mbox{for purely rotational flow} \\0 & \mbox{for pure shear flow} \\1 & \mbox{for purely elongational flow},\end{array}\right.}\) 
